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Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function

Author

Listed:
  • Walter Briec

    (UPVD - Université de Perpignan Via Domitia)

  • Kristiaan Jesourd Jean-Baptiste Kerstens

Abstract

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier.

Suggested Citation

  • Walter Briec & Kristiaan Jesourd Jean-Baptiste Kerstens, 2004. "Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function," Post-Print hal-05623484, HAL.
    • Handle: RePEc:hal:journl:hal-05623484
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